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HW4 - Homework#4 due February 11 at noon ECE 15a(2p 1 Draw...

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Homework #4 January 30, 2008 1 Homework #4 due February 11 at noon ECE 15a Winter 2008 (2p) 1. Draw a Venn diagram illustrating the operation. 2. Write the following in terms of (XOR) and (AND) only: (5p) (a) p+q (5p) (b) (p+q)(p’+q’) 3. A set of gates is said to be functionally complete (or universal) if and only if every Boolean function can be realized entirely by means of gates from this set. (a)(7p) Prove that the f-gate defined as f(A,B,C) = AB’C+BC’+A’C’ is a universal gate. (Hint: Build NOT, AND, OR gates using only the f-gates) (b) (6p) Build a 2-input XOR gate from the f-gates defined above. (4p) 4. Show that xy+yz+zx=xy+xy’z+x’yz
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